The invention pertains to the synthesis of various types of hysteresis, and in particular the synthesis of hysteresis operations for use in controllers, the synthesis of advanced form of hysteresis, and the advanced synthesized hysteresis for various applications such as signal processing, controllers, music, and computer simulations as may be used in physics, engineering, economics, as well as other areas.
Hysteresis occurs in many aspects and types of physical processes [A]. In mechanical engineering hysteresis occurs in gears and other mechanical structures. Many types of familiar [B] and newly emergent [C] magnetic materials and devices exhibit various forms of magnetization hysteresis.
Hysteresis also occurs in other types of physical processes, particularly phase transition processes [D] (including self-organizing criticality) as is well known but also notably in optical processes [E, F], some of which exhibit unusually shaped hysteresis curves [G], as well as friction, fluidics, hydrology, bilogy, and superconditivity.
Hysteresis also occurs in financial and economic systems (for example, often occurring in modeling the effects of unemployment in an economy) [,H,I,J,K]. In the inventor's own work, hysteresis can occur in economic systems (as well as the abstractions of transaction costs as applied to communications, computers, and manufacturing systems) in responses to or control of transaction costs.
Many systems and applications include electronic or computer control systems that operate on hysteretic subsystems or processes, and the hysteretic behavior complicates the design and operations of those control systems [L,M]. Many forms of sophisticated optimal control extend into control arrangements that involve hysteresis, as do simple household thermostats. Hysteresis processes also arise in game theory.
In electronics, hysteresis processes have historically been utilized in noise-rejection circuits (Schmitt triggers) and non-linear oscillators. Electronic transformers and inductors inherently exhibit electrical hysteresis effects due to the natural hysteretic properties of the materials used to make the transformer core. More profoundly, the theoretically predicted (Leon Chua) and recently perfect (Stanley Williams and team) memistor, the “fourth” passive circuit element [N], exhibits hysteresis processes (including the noteworthy “pinched” form of hysteresis curve) [O,P]. Hysteresis processes are also employed in the design and operation of certain types of electrical AC-powered synchronous motors used to render stable exact speeds.
In electronic vacuum-tube electric guitar amplifiers, hysteresis occurs in overdriven vacuum-tube amplifier output transformers due to the natural hysteretic properties of the materials used to make the transformer core and is a component (among many) of overdriven electric guitar vacuum-tube amplifier distortion that has become an essential aspect of contemporary popular music worldwide for many decades.
Mathematically, hysteresis effects are effectively a type of bifurcation and are closely related to subjects such as catastrophe theory [Q]. Even simple hysteresis models can comprise tremendously extensive and intriguing families of behaviors. The modeling, study, and generalizations of hysteresis phenomena and nonlinear differential equations that possess them has been and remains a deep and interesting area of study, involving sophisticated mathematical techniques, tools, elements, and structures including differential inclusions, linear and nonlinear operator theory, singular perturbations, differential representations, linear and nonlinear spectral theory, topological degree, Poincare maps, cellular and differential automata, nural network representations, fractional calculus and fractional-order integral/differential equations (in modeling, a source of hysteresis, and as a superior type of control system compensator for systems with input hysteresis), and fractal analysis [A,R,S,T,U,V,W,X].
Set against this background, the present invention provides a number of innovative steps of commercial value to real-time systems, control systems, numerical simulations of system, signal processing, music audio, and other applications.
In partial relation to the present invention, the inventor has found that more generally hysteresis effects in waveform distortion and waveform shaping processes can create valuable amplitude-varying spectral effects of particular interest in musical sound synthesis and musical signal processing. Further in partial relation to the present invention, the inventor has found that time-variation or modulation of parameters controlling parameterized synthesized hysteresis also create valuable spectral effects.
Additionally, such parameterized synthesized hysteresis as developed for the above and other applications appear to be valuable as control systems elements and as “metamodeling” elements within numerical system simulations.
Further, in that natural hysteresis effects in practice exhibit inherent multiple-input aspects, and often multiple-output aspects, it is useful to further extend the synthesis of hysteresis to encompass the synthesis of vector hysteresis processes.